English has its “silent e” at the end of many words. Specifically, many common English words end in -ve, like have and give. The e is silent, so these words end in a [v] sound.
And, also, many common English words begin with an [f] sound, like, um, freedom and fursuit. So it’s totally normal to produce [v] and [f] vocally with nothing in between.
We may remember the George Michael lyric, “I gotta have faith.” That’s an example. Native speakers don’t have a problem with this.
But then, Wikipedia (I know, it’s the most reliable and truthy source there is) gives “have to” [hæftə] as an example where devoicing happens in rapid speech. When you quickly say “I have faith that I don’t devoice my v’s” - is it still true, or does that apply only when you speak slowly and enunciate clearly?
Personally, when I say your sentence out loud, I elide the h in have rather than the v.
“I 'av FAITH that I DON’T deVOICE my V’s.”
I listened closely to myself to see if I was doing something weird with the [t] and the [d] in “don’t devoice” and I’m pronouncing both of those as well.
I think this is normal in English. We use a lot of consonants. It is a dense language.